Permittivity measurement with uncertainty quantification in cement-based composites using ENNreg-ANet and high-frequency electromagnetic waves

Despite the widespread adoption of high-frequency electromagnetic waves (HF-EMWs) for permittivity measurement in cement-based composites, the approach still faces the problem of aleatory and epistemic uncertainty owing to material heterogeneity and EMW diffraction. This study has proposed a deep neural network in evidence theory (ET) to measure the permittivity of cement-based composites with uncertainty quantification. In the model, an encoder-decoder module first denoises observed HF-EMWs, which captures the intuition of aleatory uncertainty in the measurements. The observed and denoised waves are then fed into an ET-based regression layer to compute the permittivity, representing the measurement's epistemic uncertainty. Finally, the permittivity measurements in a region are aggregated by a generalized Dempster's rule, which characterizes the region permittivity using an interval with uncertainty quantification. Experiments on three HF-EMW datasets demonstrate that the proposed model measures permittivity with a MSE of 10.48% in three composites with various material conditions.